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1.
Summary Approximate solutions of the B-G-K model equation are obtained for the structure of a plane shock, using various moment methods and a least squares technique. Comparison with available exact solution shows that while none of the methods is uniformly satisfactory, some of them can provide accurate values for the density slope shock thickness n . A detailed error analysis provides explanations for this result. An asymptotic analysis of n for largeMach numbers shows that it scales with theMaxwell mean free path on the hot side of the shock, and that their ratio is relatively insensitive to the viscosity law for the gas.
Näherungsweise Lösungen für die Struktur von Stoßwellen
Zusammenfassung Unter Verwendung verschiedener Momentenmethoden und der Methode der kleinsten Quadrate werden Näherungslösungen der Gleichung des B-G-K-Modells für die Struktur eines ebenen Stoßes erhalten. Der Vergleich mit der verfügbaren exakten Lösung zeigt, daß zwar keine der Methoden durchwegs befriedigend ist, einige von ihnen aber genaue Werte für die Dichteanstiegs-Dicke n des Stoßes liefern. Eine genaue Fehleruntersuchung gibt Erklärungen für dieses Ergebnis. Die asymptotische Analyse der Dicke n für großeMachzahlen zeigt, daß sie mit derMaxwellschen mittleren freien Weglänge auf der heißen Seite des Stoßes vergleichbar ist und daß der Quotient aus beiden verhältnismäßig unempfindlich gegen das Viskositätsgesetz des Gases ist.


With 7 Figures  相似文献   

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T. Hirschler  W. Gretler 《Acta Mechanica》2002,154(1-4):159-177
Summary In this paper the influence of radiation upon the classical adiabatic self-similar solution of a converging spherical shock wave is investigated. The medium is assumed to be an optically thick, inviscid and ideal gas with a constant ratio of specific heats. In front of the shock wave it is considered to be uniform and at rest, and its counter pressure is neglected. The presented paper restricts itself to presenting those similarity solutions which show the least possible deviation from the classical adiabatic solution. Their eigenvalues are determined numerically and listed. The flow profiles of nonadiabatic similarity solutions are shown and compared with the flow profiles of the adiabatic similarity solution.  相似文献   

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Although the nonlinear diffusion equation has been extensively studied and there exists substantial literature in many diverse areas of science and technology, the number of exact concentration profiles is nevertheless limited. In a recent article in this journal (Hill [1]) a brief review of known exact results is given, as well as an elementary integration procedure which appears to be a general device for obtaining integrals associated with similarity solutions. This paper extends the results given in [1] and for particular power law diffusivitiesc m (such asm = –/12, –1, –/32 and –2) presents a number of new exact solutions obtained by fully integrating the ordinary differential equations derived in [1]. In addition new results are found for a general nonlinear diffusion equation which includes one-dimensional diffusion with an inhomogenouus and nonlinear diffusivityc mxmas well as symmetric nonlinear diffusion in cylinders and spheres. Moreover by a separate and ad-hoc procedure a new solution is obtained of the travelling wave type but with a variable wave speed. Some of the new exact solutions obtained for one-dimensional nonlinear diffusion with power law diffusivitiesc mare illustrated graphically.  相似文献   

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The attenuation factor for a pressure wave generated by water hammer in the flow of a weak polyacrylamide solution is determined experimentally.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 6, pp. 1045–1049, December, 1973.  相似文献   

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Further results are given on the experimental determination of the attenuation of a pressure wave in weak polymer solutions.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 6, pp. 1050–1051, December, 1973.  相似文献   

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In this paper an attempt is made to study the propagation of weak shock waves in a thermoelastic material that does not conduct heat. We study the velocity of propagation of such shocks. We derive and study the equations governing the growth and decay of plane shocks and shocks of arbitrary form.  相似文献   

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Similarity solutions for slender dry patches with thermocapillarity   总被引:2,自引:0,他引:2  
The lubrication approximation is used to investigate slender dry patches in an infinitely wide film of viscous fluid flowing steadily on an inclined plane that is either heated or cooled relative to the surrounding atmosphere. Four non-isothermal situations in which thermocapillary effects play a significant role are considered.Similarity solutions describing a thermocapillary-driven flow with a dry patch that is widening or narrowing due to either gravitational or surface-tension effects on a non-uniformly heated or cooled substrate are obtained, and examples of these solutions, when the substrate temperature gradient depends on the longitudinal coordinate according to a general power law, are presented. When gravitational effects are strong, the solution contains a free parameter, and for each value of this parameter there is a unique solution representing both a narrowing pendent dry patch and a widening sessile dry patch, whose transverse profile has a monotonically increasing shape. When surface-tension effects are strong, the solution also contains a free parameter, and for each value of this parameter there is both a unique solution representing a narrowing dry patch, whose transverse profile has a monotonically increasing shape, and a one-parameter family of solutions representing a widening dry patch, whose transverse profile has a capillary ridge near the contact line and decays in an oscillatory manner far from it.Similarity solutions are also obtained for both a gravity-driven and a constant-surface-shear-stress-driven flow with a dry patch that is widening or narrowing due to thermocapillarity on a uniformly heated or cooled substrate. The solutions in both cases contain a free parameter, and for each value of this parameter there is a unique solution representing both a narrowing dry patch on a heated substrate and a widening dry patch on a cooled substrate, whose transverse profile has a monotonically increasing shape.  相似文献   

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Diamond synthesis by weak shock loading   总被引:1,自引:0,他引:1  
A hexagonal polymorph of diamond has been synthesized by relatively weak shock loading (in a range of projectile velocity 0.655 to 1.88 km sec–1) with a recovery technique. Four mixtures of copper with spectroscopic graphite, amorphous carbon, glassy carbon and graphite fluoride, with densities of 4.8 to 7.8 g cm–3, were used to control the shock temperature rise and to quench efficiently. Spectroscopic graphite gave the maximum yield of diamond (8%). Chaoite was also observed in the shocked amorphous carbon and glassy carbon. A local temperature rise during shock was inferred from the temperature of some spherical particles, indicative of superheating of the particles to near or above the melting point.  相似文献   

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T. Fang 《Acta Mechanica》2003,163(3-4):161-172
In this paper, the thermal boundary-layer problem of a semi-infinite flat plate moving in a constant velocity free stream is studied. The similarity equations with viscous dissipation for the thermal boundary-layer are derived and solved by numerical techniques. Under some specific conditions, the thermal boundary-layer similarity equation can be integrated analytically. The results are analyzed for very small Eckert number case and large Eckert number case. It is found that, for the two cases, wall heat fluxes will increase with the increase of the velocity ratio . With increasing Eckert number, the viscous dissipation heating will become dominant. However, for the Prandtl number when the Eckert number is small, it is found that wall heat fluxes will increase with increasing Prandtl number only for a certain range of velocity ratio . For the other range, the wall heat fluxes will have a maximum at a certain Prandtl number, and, when the Prandtl number is larger than the critical value, wall heat fluxes will decrease with increasing Prandtl number. Some examples of the lower solution branch are also presented to compare with the upper solution branch. It is found that the lower solution branch will result in lower heat fluxes at the wall.  相似文献   

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This paper presents a novel integral-equation technique for solving the steady-state wave-resistance problem. The free-surface condition is linearized, but the body condition is satisfied exactly. An integral relation describing the flow inside an arbitrarily truncated internal region is first obtained by applying Green's Theorem, using only the simple source function for an infinite fluid. The internal flow is next matched with eigen expansions in the upstream and downstream outer regions. The radiation condition can be satisfied exactly simply by a proper choice of the solution form in these outer regions. The method is applied to investigate flows about both lifting and non-lifting two-dimensional bodies. Agreement with existing results is excellent. The present formulation provides a simple yet rational basis for tackling the practical three-dimensional ship-wave problem, in which past workers have encountered considerable difficulties using a complicated free-surface Green function.  相似文献   

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This paper describes the fundamental principles of the mathematical method used by the authors in discussing the direct geophysical problem of analysing the behaviour of the Atlantic continental margin of the Iberian Peninsula as a transmission medium of seismic energy. In order to resolve this problem, a weak variational formulation is proposed, building up an approximate solution by means of a semidiscrete treatment with the finite element method. The excitation of that non-subductive ocean-continent transition zone is supposed to be caused by Love waves normally incident at the continental boundary. The physical and geometrical parameters describing the model are obtained using as a starting point the experimental data known for this zone. The work shows the main results that we have obtained, the geophysical interpretation of which can be seen in Reference 1. Finally we proposed a large variety of open problems to which analogous techniques can be applied, owing to the extended validity of the proposed method.  相似文献   

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H. Hamad  F. El-Fayes 《Acta Mechanica》1996,119(1-4):53-63
Summary The structure of one dimensional shock waves is investigated using the Navier-Stokes equations for the gas phase and the particle phase. The resulting system of four ordinary nonlinear differential equations is reduced to a system of two autonomous nonlinear differential equations which are solved analytically. This solution is obtained formally by neglecting the viscosity (=0).  相似文献   

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The similarity solutions of a strong shock wave propagation in a mixture of a gas and small solid particles have been investigated. Similarity solution exists only when the shock is very strong and the surrounding medium is of a constant density and at rest and with negligible counterpressure. The non-dimensional fundamental equations are derived and studied. The results depend on three non-dimensional parameters; i.e. (i) the ratio of the specific heats of the gas γ, (ii) the mass concentration of the solid particles kp in the mixture and (iii) the ratio of the density of the solid to that of initial density of the gas G. Numerical solutions for various values of γ kp and G are presented and discussed. The speeds of the shock wave front and its location with various energy releases are given.  相似文献   

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Consideration is given to non-stationary shock wave on spallation. Spall strength can be written as (i) pressure — particle velocity diagram in a one-dimensional case, and (ii) pressure — angle of turn flow diagram in a two-dimensional case. Experimental procedure involves (i) loading of the explosive by sliding detonation and (ii) orthogonal flash X-raying. In this way, some metals in particular low-melting ones and plastics as well as liquids have been studied based on the present results and those of other researchers. The dependences of spall strength — deformation rate have been obtained for substances studied in the form of power or linear functions. Some aspects of spallation and of accompanying effects on the base relations obtained are discussed.  相似文献   

17.
Fundamental solutions in the form of free-space Green's functions are developed for a class of two-dimensional, variable density elastodynamic problems. These fundamental solutions are evaluated by means of a coordinate transformation based on conformal mapping in conjunction with wave decomposition, which allows for both vertical and lateral heterogeneities, and can be used within the context of a boundary integral equation formulation analogous to that originally proposed by Cruse and Rizzo (J Math Anal Appl 22 (1968) 244). Finally, a numerical example serves to illustrate the methodology developed herein.  相似文献   

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Summary The present paper investigates similarity solutions for the two-dimensional flow of a mass of cohesionless granular material down rough curved beds having gradually varying slopes. The work is relevant to the motion of rockfalls and loose snow flow avalanches. The depth and velocity profiles for the moving mass are determined in analytical form and the evolution equation for the total length of the pile is integrated numerically using a Runge-Kutta technique. Although similarity solutions can occur for general bed shapes (as long as the curvature is small), specific computations are performed here for two families of bed profiles, one which is in the shape of a circular arc and the other in which the slope decays exponentially with downstream distance. The pile of granular material starts from rest, initially accelerates and then decelerates, finally coming to rest as a result of bed friction and the gradually decreasing bed slope. Depending upon the frictional parameters, the shape of the bed and the initial depth to length of the pile, it is found that the variation of total length with time can exhibit different behaviours. The pile can grow monotonically, it can asymptote to a constant length, it can grow to a maximum and then decrease or it can decrease to a minimum and then increase with time. Furthermore, there are regions in parameter space for which the pile moves as a rigid body either for the whole time of travel or for portions of it.on leave from Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke St. W., Montreal H3A 2K6, Canadaon leave from Institute of Snow and Ice Studies, N.R.C.D.P., Suyoshi, Nagaoka-shi, 940, JapanWith 7 Figures  相似文献   

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